Is this a Function? \( D: 3,6,6,12,18 \) \( R: 7,5,10,9,10 \)

To determine whether the given relation is a function, let's analyze the provided sets: - **Domain (D):** 3, 6, 6, 12, 18 - **Range (R):** 7, 5, 10, 9, 10 ### Understanding Functions A **function** is a relation where **each element in the domain is associated with exactly one element in the range**. This means: 1. **Every input has an output:** No element in the domain is left without a corresponding element in the range. 2. **No input has multiple outputs:** Each element in the domain is paired with one and only one element in the range. ### Analyzing the Given Relation Let's pair the elements of the domain (D) with the range (R) based on their positions: 1. **3 → 7** 2. **6 → 5** 3. **6 → 10** 4. **12 → 9** 5. **18 → 10** ### Identifying Issues - **Repeated Input with Different Outputs:** The number **6** appears **twice** in the domain but is associated with two **different** outputs: **5** and **10**. This violates the second rule of functions, where each input should map to only one output. ### Conclusion Since the input **6** is associated with two different outputs (**5** and **10**), the given relation **is not a function**. **Final Answer:** No. The input value 6 is paired with both 5 and 10, so each input does not have exactly one output.